Applied Mathematics Commons^™

Closed-Range Composition Operators On Weighted Bergman Spaces And Applications, Shanda Renee Fulmer

Graduate Theses and Dissertations

We will discuss necessary and sufficient conditions for a Composition Operator to be closed range on the weighted Bergman spaces. The function phi is an analytic self map of the unit disk and our results extend those previously intended for the classical Bergman space. We will also give applications.

An Applied Functional And Numerical Analysis Of A 3-D Fluid-Structure Interactive Pde, Thomas J. Clark

Department of Mathematics: Dissertations, Theses, and Student Research

We will present qualitative and numerical results on a partial differential equation (PDE) system which models a certain fluid-structure dynamics. In Chapter \ref{ChWellposedness}, the wellposedness of this PDE model is established by means of constructing for it a nonstandard semigroup generator representation; this representation is essentially accomplished by an appropriate elimination of the pressure. This coupled PDE model involves the Stokes system which evolves on a three dimensional domain $\mathcal{O}$ being coupled to a fourth order plate equation, possibly with rotational inertia parameter $\rho >0$, which evolves on a flat portion $\Omega$ of the boundary of $\mathcal{O}$. The coupling on …

Generating Combinatorial Objects- A New Perspective, Alexander Chizoma Nwala

Computer Science Theses & Dissertations

Combinatorics is the science of "possibilities." This definition, while not formal is a fair statement because all too often, in order to gain insight into the solution of many counting problems, we explore the possibilities. In some cases we seek to know how many options, while in other cases we seek to enumerate or list the options. Irrespective of the scenario, combinatorics plays a vital role today. In many instances such as exploring the options for choosing a new password for a combination lock, we employ combinatorics. In considering the possible license plate permutations for a state, or to see …

High Frequency Data: Modeling Durations Via The Acd And Log Acd Models, Lilian Cheung

Honors Scholar Theses

This thesis proposes a method of finding initial parameter estimates in the Log ACD₁ model for use in recursive estimation. The recursive estimating equations method is applied to the Log ACD₁ model to find recursive estimates for the unknown parameters in the model. A literature review is provided on the ACD and Log ACD models, and on the theory of estimating equations. Monte Carlo simulations indicate that the proposed method of finding initial parameter estimates is viable. The parameter estimation process is demonstrated by fitting an ACD model and a Log ACD model to a set of IBM …

Physiologically-Based Pharmacokinetic Model For Ertapenem, Whitney Forbes

Electronic Theses and Dissertations

Ertapenem is a carbapenem used to treat a wide range of bacterial infections. What sets ertapenem apart from other carbapenems is its longer half-life which implies it need only be administered once daily. We developed a physiologically-based pharmacokinetic model for the distribution of ertapenem within the body. In the model, parameters such as human body weight and height, age, organ volumes, blood flow rates, and partition coefficients of particular tissues are used to examine the absorption, distribution, metabolism, and excretion of ertapenem. The total and free blood concentrations found were then compared to experimental data. We then examined the sensitivity …

Are Highly Dispersed Variables More Extreme? The Case Of Distributions With Compact Support, Benedict E. Adjogah

Electronic Theses and Dissertations

We consider discrete and continuous symmetric random variables X taking values in [0; 1], and thus having expected value 1/2. The main thrust of this investigation is to study the correlation between the variance, Var(X) of X and the value of the expected maximum E(Mn) = E(X1,...,Xn) of n independent and identically distributed random variables X1,X2,...,Xn, each distributed as X. Many special cases are studied, some leading to very interesting alternating sums, and some progress is made towards a general theory.

A Radial Basis Function Partition Of Unity Method For Transport On The Sphere, Kevin Aiton

Boise State University Theses and Dissertations

The transport phenomena dominates geophysical fluid motions on all scales making the numerical solution of the transport problem fundamentally important for the overall accuracy of any fluid solver. In this thesis, we describe a new high-order, computationally efficient method for numerically solving the transport equation on the sphere. This method combines radial basis functions (RBFs) and a partition of unity method (PUM). The method is mesh-free, allowing near optimal discretization of the surface of the sphere, and is free of any coordinate singularities. The basic idea of the method is to start with a set of nodes that are quasi-uniformly …

The Intelligent Driver Model: Analysis And Application To Adaptive Cruise Control, Rachel Malinauskas

All Theses

There are a large number of models that can be used to describe traffic flow. Although some were initially theoretically derived, there are many that were constructed with utility alone in mind. The Intelligent Driver Model (IDM) is a microscopic model that can be used to examine traffic behavior on an individual level with emphasis on the relation to an ahead vehicle. One application for this model is that it is easily molded to performing the operations for an Adaptive Cruise Control (ACC) system. Although it is clear that the IDM holds a number of convenient properties, like easily interpreted …

General Sampling Schemes For The Bergman Spaces, Newton Foster

Graduate Theses and Dissertations

A characterization of sampling sequences for the Bergman spaces was originally provided by Seip and later expanded upon by Schuster. We consider a generalized notion of sampling using the infimum norm of the quotient space. Adapting some old techniques, we provide a characterization of general sampling sequences in terms of the lower uniform density.

Spatial Scheduling Algorithms For Production Planning Problems, Sudharshana Srinivasan

Theses and Dissertations

Spatial resource allocation is an important consideration in shipbuilding and large-scale manufacturing industries. Spatial scheduling problems (SSP) involve the non-overlapping arrangement of jobs within a limited physical workspace such that some scheduling objective is optimized. Since jobs are heavy and occupy large areas, they cannot be moved once set up, requiring that the same contiguous units of space be assigned throughout the duration of their processing time. This adds an additional level of complexity to the general scheduling problem, due to which solving large instances of the problem becomes computationally intractable. The aim of this study is to gain a …

Experimental Evidence For Heterogeneous Expectations In A Simple New Keynesian Framework, Atticus David Holm Graven

Business and Economics Honors Papers

This paper is a two-dimensional analysis of agent behavior in a standard New Keynesian (NK) Macroeconomic model. On the dimension of pure mathematics, we analyze the parameters of the NK model and of possible prediction rules. On the other dimension we continue a practice of empirical study of heterogeneous expectations with an experiment. The experiment will ask participants to make predictions of future output and inflation. Their responses will create a data-set upon which analysis will be performed to illuminate and corroborate current theories of economic decision making. The literature has shown that most agents' forecasting rules can be modeled …

Combinatorial And Algebraic Coding Techniques For Flash Memory Storage, Kathryn A. Haymaker

Department of Mathematics: Dissertations, Theses, and Student Research

Error-correcting codes are used to achieve reliable and efficient transmission when storing or sending information across a noisy channel. This thesis investigates a mathematical approach to coding techniques for storage devices such as flash memory storage, although many of the resulting codes and coding schemes can be applied in other contexts. The main contributions of this work include the design of efficient codes and decoding algorithms using discrete structures such as graphs and finite geometries, and developing a variety of strategies for adapting codes to a multi-level setting.

Information storage devices are prone to errors over time, and the frequency …

A Comparison Of Clustering And Missing Data Methods For Health Sciences, Ran Zhao, Deanna Needell, Christopher Johansen, Jerry L. Grenard

CMC Faculty Publications and Research

In this paper, we compare and analyze clustering methods with missing data in health behavior research. In particular, we propose and analyze the use of compressive sensing's matrix completion along with spectral clustering to cluster health related data. The empirical tests and real data results show that these methods can outperform standard methods like LPA and FIML, in terms of lower misclassification rates in clustering and better matrix completion performance in missing data problems. According to our examination, a possible explanation of these improvements is that spectral clustering takes advantage of high data dimension and compressive sensing methods utilize the …

Elliptic Curves And Cryptography, Linh Nguyen, Andrew Shallue, Faculty Advisor

John Wesley Powell Student Research Conference

No abstract provided.

In Pursuit Of The Ringel-Kotzig Conjecture: Uniform K-Distant Trees Are Graceful, Kimberly Wenger, Daniel Roberts, Faculty Advisor

John Wesley Powell Student Research Conference

Graph labeling has been an active area of research since 1967, when Rosa introduced the concept. Arguably, the biggest open conjecture in the field is referred to as the Ringel-Kotzig conjecture, which states that all trees admit a graceful labeling. In this talk, we will give a bit of background on the problem, as well as present our own results. Namely, that a certain infinite class of trees (called uniform k-distant trees) admits a graceful labeling.

Decomposing Complete Graphs Into A Graph Pair Of Order 6, Yizhe Gao, Daniel Roberts, Faculty Advisor

John Wesley Powell Student Research Conference

Firstly, a graph G consists of a vertex set V (G), and an edge set E (G) of endpoints which relate two vertices with each edge. Also, a decomposition of a graph is a list of subgraphs such that each edge appears in exactly one subgraph in the list. In the field of graph theory, graph decomposition is an active field of research. A graph pair is a pair of graphs on the same vertex set whose union is the complete graph. Abueida and Daven studied decompositions of complete graphs into graph-pairs of order four and five. We are extending …

Well-Posedness And Stability Of A Semilinear Mindlin–Timoshenko Plate Model, Pei Pei

Department of Mathematics: Dissertations, Theses, and Student Research

I will discuss well-posedness and long-time behavior of Mindlin-Timoshenko plate equations that describe vibrations of thin plates. This system of partial differential equations was derived by R. Mindlin in 1951 (though E. Reissner also considered an analogous model earlier in 1945). It can be regarded as a generalization of the Timoshenko beam model (1937) to flat plates, and is more accurate than the classical Kirchhoff-Love plate theory (1888) because it accounts for shear deformations.

I will present a semilinear version of the Mindlin-Timoshenko system. The primary feature of this model is the interplay between nonlinear frictional forces (``damping”) and nonlinear …

In Category Of Sets And Relations, It Is Possible To Describe Functions In Purely Category Terms, Vladik Kreinovich, Martine Ceberio, Quentin Brefort

Departmental Technical Reports (CS)

We prove that in the category of sets and relations, it is possible to describe functions in purely category terms.

Numerical Solutions For Problems With Complex Physics In Complex Geometry, Yifan Wang

Doctoral Dissertations

In this dissertation, two high order accurate numerical methods, Spectral Element Method (SEM) and Discontinuous Galerkin method (DG), are discussed and investigated. The advantages of both methods and their applicable areas are studied. Particular problems in complex geometry with complex physics are investigated and their high order accurate numerical solutions obtained by using either SEM or DG are presented. Furthermore, the Smoothed Particle Hydrodynamics (SPH) (a mesh-free weighted interpolation method) is implemented on graphics processing unit (GPU). Some numerical simulations of the complex flow with a free surface are presented and discussed to show the advantages of SPH method in …

Modeling And Simulation Of Shape Changes Of Red Blood Cells In Shear Flow, John Gounley

Mathematics & Statistics Theses & Dissertations

A description of the biomechanical character of red blood cells is given, along with an introduction to current computational schemes which use deformable capsules to simulate red blood cell shape change. A comprehensive two- and three-dimensional framework for the fluid-structure interaction between a deformable capsule and an ambient flow is provided. This framework is based on the immersed boundary method, using lattice Boltzmann and finite element methods for the fluid and structure, respectively. The characteristic response and recovery times of viscoelastic circular and spherical capsules are compared, and their dependence on simulation parameters is shown. The shape recovery of biconcave …